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  • POJ2533:Longest Ordered Subsequence

    Longest Ordered Subsequence


    Longest Ordered Subsequence
    Time Limit: 2000MS   Memory Limit: 65536K
    Total Submissions: 31680   Accepted: 13848

    Description

    A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence (a1a2, ..., aN) be any sequence (ai1ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8).

    Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.

    Input

    The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 <= N <= 1000

    Output

    Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

    Sample Input

    7
    1 7 3 5 9 4 8

    Sample Output

    4


    这是一道动归题。

    n=3


    1 7 3 5 9 4 8

    dp[]=0;

    1 ap[1]=0
    7 dp[2]=1
    3 dp[3]=1
    5 d[4]=2
    9 d[5]=3
    4 d[6]=2
    8 d[7]=3

    最后找出最大值然后加一;

    详细实现例如以下:


    
    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    #include<iostream>
    
    using namespace std;
    
    const int M = 1000+5;
    int sequence[M];    //输入的数据
    int dp[M];          
    
    int main()
    {
        int n;
        while(scanf("%d", &n)!=EOF)
        {
            for(int i=1; i<=n; i++)
                scanf("%d",  &sequence[i]);
            memset(dp, 0, sizeof(dp));          //初始化为0
            for(int i=1; i<=n; i++)
                for(int j=1; j<i; j++)
                {
                    if(sequence[i]>sequence[j])
                        dp[i] = max(dp[i], dp[j] + 1);    //动归方程
                }
            int ans=0;
            for(int i=1; i<=n; i++)
                ans = max(ans, dp[i]);
            printf("%d
    ", ans+1);
        }
        return 0;
    }


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  • 原文地址:https://www.cnblogs.com/mqxnongmin/p/10841138.html
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